{"id":203,"date":"2019-12-21T10:17:20","date_gmt":"2019-12-21T10:17:20","guid":{"rendered":"https:\/\/logbooks.ifosim.org\/iucaa2019\/?p=203"},"modified":"2019-12-21T10:17:20","modified_gmt":"2019-12-21T10:17:20","slug":"why-do-we-see-non-zero-common-prc-and-src-length-signals-at-the-michelsons-output-port","status":"publish","type":"post","link":"https:\/\/logbooks.ifosim.org\/iucaa2019\/2019\/12\/21\/why-do-we-see-non-zero-common-prc-and-src-length-signals-at-the-michelsons-output-port\/","title":{"rendered":"Why do we see non-zero common, PRC and SRC length signals at the Michelson&#8217;s output port?"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Question<\/h2>\n\n\n\n<p>The &#8220;Degrees of freedom transfer functions&#8221; task in notebook 14 involves applying signals to the cavity mirrors or the power recycling or signal recycling mirror to modulate the differential arm, common arm, power recycling and signal recycling cavity lengths, respectively. We look at a photodetector at the output port of the interferometer, which is demodulated at the signal frequency for each step on the x-axis.<\/p>\n\n\n\n<p>Here is the differential arm response:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Differential arm length to output port response<\/h4>\n\n\n\n<div class=\"ssl-finesse-kat-tab-panel\" style=\"width:460px\" data-img-width=\"460\" data-img-height=\"345\"><div class=\"ssl-finesse-kat-tab-panel-tab-container\" style=\"height:345px\"><div class=\"ssl-finesse-kat-tab-panel-tab ssl-finesse-kat-tab-panel-tab-selected\" data-tab=\"plot\"><div class=\"ssl-finesse-kat-plot\"><a class=\"ssl-finesse-kat-attachmenturl\" href=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-12.svg\"><img decoding=\"async\" class=\"ssl-finesse-kat-plot-img\" src=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-12.svg\"\/><\/a><\/div><\/div><div class=\"ssl-finesse-kat-tab-panel-tab\" data-tab=\"script\"><div class=\"ssl-finesse-kat-script\"><pre class=\"ssl-finesse-kat-script-input ssl-finesse-kat-script-input-display\"><code>l LI 125.0 0.0 0.0 nin\ns s1 0.0 nin nprc1\nm1 PRM 0.03 3.75e-05 90.0 nprc1 nprc2\ns prc 53.0 nprc2 nbsin\nbs bs1 0.5 0.5 0.0 45.0 nbsin n0y n0x nbsout\ns sx 4.5 n0x n1x\nm1 ITMX 0.014 3.75e-05 90.0 n1x n2x\nattr ITMX mass 40.0\ns Lx 3995.0 n2x n3x\nm1 ETMX 0.0 3.75e-05 90.0 n3x n4x\nattr ETMX mass 40.0\ns sy 4.45 n0y n1y\nm1 ITMY 0.014 3.75e-05 0.0 n1y n2y\nattr ITMY mass 40.0\ns Ly 3995.0 n2y n3y\nm1 ETMY 0.0 3.75e-05 0.0 n3y n4y\nattr ETMY mass 40.0\ns src 50.525 nbsout nsrc1\nm1 SRM 0.2 3.75e-05 90.0 nsrc1 nout\nl LO 1.0 0.0 90.0 nLO2\ns sLO1 0.0 nout nLO3\nbs bsLO 0.5 0.5 0.0 0.0 nLO3 nHD1 nHD2 nLO2\nhd TF 180.0 nHD1 nHD2\nxaxis sig f log 10 10000 1000\nfsig sig ETMX z 1.0 0.0 1.0\nfsig sig ETMY z 1.0 180.0 1.0\nyaxis log abs<\/code><\/pre><\/div><\/div><\/div><ul class=\"ssl-finesse-kat-tab-panel-tabs\"><li class=\"ssl-finesse-kat-tab-panel-tab-link ssl-finesse-kat-tab-panel-tab-link-selected\" data-tab=\"plot\">Plot<\/li><li class=\"ssl-finesse-kat-tab-panel-tab-link\" data-tab=\"script\">Script<\/li><\/ul><\/div>\n\n\n\n<p>The response is 1 \u00d7 10^11 W\/m at low frequencies, i.e. very strong. This is expected since the Michelson is configured to sit at the dark fringe condition and therefore couples differential arm length changes most strongly to the output port. So this looks good.<\/p>\n\n\n\n<p>The problem is that when we modulate the other degrees of freedom, we still see a non-zero signal at the same port. Here is the common arm length change:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Common arm length to output port response<\/h4>\n\n\n\n<div class=\"ssl-finesse-kat-tab-panel\" style=\"width:460px\" data-img-width=\"460\" data-img-height=\"345\"><div class=\"ssl-finesse-kat-tab-panel-tab-container\" style=\"height:345px\"><div class=\"ssl-finesse-kat-tab-panel-tab ssl-finesse-kat-tab-panel-tab-selected\" data-tab=\"plot\"><div class=\"ssl-finesse-kat-plot\"><a class=\"ssl-finesse-kat-attachmenturl\" href=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-13.svg\"><img decoding=\"async\" class=\"ssl-finesse-kat-plot-img\" src=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-13.svg\"\/><\/a><\/div><\/div><div class=\"ssl-finesse-kat-tab-panel-tab\" data-tab=\"script\"><div class=\"ssl-finesse-kat-script\"><pre class=\"ssl-finesse-kat-script-input ssl-finesse-kat-script-input-display\"><code>l LI 125.0 0.0 0.0 nin\ns s1 0.0 nin nprc1\nm1 PRM 0.03 3.75e-05 90.0 nprc1 nprc2\ns prc 53.0 nprc2 nbsin\nbs bs1 0.5 0.5 0.0 45.0 nbsin n0y n0x nbsout\ns sx 4.5 n0x n1x\nm1 ITMX 0.014 3.75e-05 90.0 n1x n2x\nattr ITMX mass 40.0\ns Lx 3995.0 n2x n3x\nm1 ETMX 0.0 3.75e-05 90.0 n3x n4x\nattr ETMX mass 40.0\ns sy 4.45 n0y n1y\nm1 ITMY 0.014 3.75e-05 0.0 n1y n2y\nattr ITMY mass 40.0\ns Ly 3995.0 n2y n3y\nm1 ETMY 0.0 3.75e-05 0.0 n3y n4y\nattr ETMY mass 40.0\ns src 50.525 nbsout nsrc1\nm1 SRM 0.2 3.75e-05 90.0 nsrc1 nout\nl LO 1.0 0.0 90.0 nLO2\ns sLO1 0.0 nout nLO3\nbs bsLO 0.5 0.5 0.0 0.0 nLO3 nHD1 nHD2 nLO2\nhd TF 180.0 nHD1 nHD2\nxaxis sig f log 10 10000 1000\nfsig sig ETMX z 1.0 0.0 1.0\nfsig sig ETMY z 1.0 0.0 1.0\nyaxis log abs<\/code><\/pre><\/div><\/div><\/div><ul class=\"ssl-finesse-kat-tab-panel-tabs\"><li class=\"ssl-finesse-kat-tab-panel-tab-link ssl-finesse-kat-tab-panel-tab-link-selected\" data-tab=\"plot\">Plot<\/li><li class=\"ssl-finesse-kat-tab-panel-tab-link\" data-tab=\"script\">Script<\/li><\/ul><\/div>\n\n\n\n<p>The signal is definitely not zero, rather it&#8217;s just over 2500 W\/m at low frequencies.<\/p>\n\n\n\n<p>The PRC and SRC length responses below are almost zero at low frequencies, but not quite zero.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Power recycling cavity length to output port response<\/h4>\n\n\n\n<div class=\"ssl-finesse-kat-tab-panel\" style=\"width:460px\" data-img-width=\"460\" data-img-height=\"345\"><div class=\"ssl-finesse-kat-tab-panel-tab-container\" style=\"height:345px\"><div class=\"ssl-finesse-kat-tab-panel-tab ssl-finesse-kat-tab-panel-tab-selected\" data-tab=\"plot\"><div class=\"ssl-finesse-kat-plot\"><a class=\"ssl-finesse-kat-attachmenturl\" href=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-14.svg\"><img decoding=\"async\" class=\"ssl-finesse-kat-plot-img\" src=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-14.svg\"\/><\/a><\/div><\/div><div class=\"ssl-finesse-kat-tab-panel-tab\" data-tab=\"script\"><div class=\"ssl-finesse-kat-script\"><pre class=\"ssl-finesse-kat-script-input ssl-finesse-kat-script-input-display\"><code>l LI 125.0 0.0 0.0 nin\ns s1 0.0 nin nprc1\nm1 PRM 0.03 3.75e-05 90.0 nprc1 nprc2\ns prc 53.0 nprc2 nbsin\nbs bs1 0.5 0.5 0.0 45.0 nbsin n0y n0x nbsout\ns sx 4.5 n0x n1x\nm1 ITMX 0.014 3.75e-05 90.0 n1x n2x\nattr ITMX mass 40.0\ns Lx 3995.0 n2x n3x\nm1 ETMX 0.0 3.75e-05 90.0 n3x n4x\nattr ETMX mass 40.0\ns sy 4.45 n0y n1y\nm1 ITMY 0.014 3.75e-05 0.0 n1y n2y\nattr ITMY mass 40.0\ns Ly 3995.0 n2y n3y\nm1 ETMY 0.0 3.75e-05 0.0 n3y n4y\nattr ETMY mass 40.0\ns src 50.525 nbsout nsrc1\nm1 SRM 0.2 3.75e-05 90.0 nsrc1 nout\nl LO 1.0 0.0 90.0 nLO2\ns sLO1 0.0 nout nLO3\nbs bsLO 0.5 0.5 0.0 0.0 nLO3 nHD1 nHD2 nLO2\nhd TF 180.0 nHD1 nHD2\nxaxis sig f log 10 10000 1000\nfsig sig PRM z 1.0 0.0 1.0\nyaxis log abs<\/code><\/pre><\/div><\/div><\/div><ul class=\"ssl-finesse-kat-tab-panel-tabs\"><li class=\"ssl-finesse-kat-tab-panel-tab-link ssl-finesse-kat-tab-panel-tab-link-selected\" data-tab=\"plot\">Plot<\/li><li class=\"ssl-finesse-kat-tab-panel-tab-link\" data-tab=\"script\">Script<\/li><\/ul><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Signal recycling cavity length to output port response<\/h4>\n\n\n\n<div class=\"ssl-finesse-kat-tab-panel\" style=\"width:460px\" data-img-width=\"460\" data-img-height=\"345\"><div class=\"ssl-finesse-kat-tab-panel-tab-container\" style=\"height:345px\"><div class=\"ssl-finesse-kat-tab-panel-tab ssl-finesse-kat-tab-panel-tab-selected\" data-tab=\"plot\"><div class=\"ssl-finesse-kat-plot\"><a class=\"ssl-finesse-kat-attachmenturl\" href=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-15.svg\"><img decoding=\"async\" class=\"ssl-finesse-kat-plot-img\" src=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-15.svg\"\/><\/a><\/div><\/div><div class=\"ssl-finesse-kat-tab-panel-tab\" data-tab=\"script\"><div class=\"ssl-finesse-kat-script\"><pre class=\"ssl-finesse-kat-script-input ssl-finesse-kat-script-input-display\"><code>l LI 125.0 0.0 0.0 nin\ns s1 0.0 nin nprc1\nm1 PRM 0.03 3.75e-05 90.0 nprc1 nprc2\ns prc 53.0 nprc2 nbsin\nbs bs1 0.5 0.5 0.0 45.0 nbsin n0y n0x nbsout\ns sx 4.5 n0x n1x\nm1 ITMX 0.014 3.75e-05 90.0 n1x n2x\nattr ITMX mass 40.0\ns Lx 3995.0 n2x n3x\nm1 ETMX 0.0 3.75e-05 90.0 n3x n4x\nattr ETMX mass 40.0\ns sy 4.45 n0y n1y\nm1 ITMY 0.014 3.75e-05 0.0 n1y n2y\nattr ITMY mass 40.0\ns Ly 3995.0 n2y n3y\nm1 ETMY 0.0 3.75e-05 0.0 n3y n4y\nattr ETMY mass 40.0\ns src 50.525 nbsout nsrc1\nm1 SRM 0.2 3.75e-05 90.0 nsrc1 nout\nl LO 1.0 0.0 90.0 nLO2\ns sLO1 0.0 nout nLO3\nbs bsLO 0.5 0.5 0.0 0.0 nLO3 nHD1 nHD2 nLO2\nhd TF 180.0 nHD1 nHD2\nxaxis sig f log 10 10000 1000\nfsig sig SRM z 1.0 0.0 1.0\nyaxis log abs<\/code><\/pre><\/div><\/div><\/div><ul class=\"ssl-finesse-kat-tab-panel-tabs\"><li class=\"ssl-finesse-kat-tab-panel-tab-link ssl-finesse-kat-tab-panel-tab-link-selected\" data-tab=\"plot\">Plot<\/li><li class=\"ssl-finesse-kat-tab-panel-tab-link\" data-tab=\"script\">Script<\/li><\/ul><\/div>\n\n\n\n<p>Our first hypothesis was that the asymmetries between the arms led to coupling between the bright and dark ports of the main Michelson beam splitter. Removing the difference in length between the beam splitter and ITMs in both arms gets rid of most of the signal in the common arm length signal at the output port, but we still see non-zero signal (similarly, PRC and SRC signals are also still non-zero):<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Common arm length to output port response<\/h4>\n\n\n\n<div class=\"ssl-finesse-kat-tab-panel\" style=\"width:460px\" data-img-width=\"460\" data-img-height=\"345\"><div class=\"ssl-finesse-kat-tab-panel-tab-container\" style=\"height:345px\"><div class=\"ssl-finesse-kat-tab-panel-tab ssl-finesse-kat-tab-panel-tab-selected\" data-tab=\"plot\"><div class=\"ssl-finesse-kat-plot\"><a class=\"ssl-finesse-kat-attachmenturl\" href=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-16.svg\"><img decoding=\"async\" class=\"ssl-finesse-kat-plot-img\" src=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-16.svg\"\/><\/a><\/div><\/div><div class=\"ssl-finesse-kat-tab-panel-tab\" data-tab=\"script\"><div class=\"ssl-finesse-kat-script\"><pre class=\"ssl-finesse-kat-script-input ssl-finesse-kat-script-input-display\"><code>l LI 125.0 0.0 0.0 nin\ns s1 0.0 nin nprc1\nm1 PRM 0.03 3.75e-05 90.0 nprc1 nprc2\ns prc 53.0 nprc2 nbsin\nbs bs1 0.5 0.5 0.0 45.0 nbsin n0y n0x nbsout\ns sx 4.5 n0x n1x\nm1 ITMX 0.014 3.75e-05 90.0 n1x n2x\nattr ITMX mass 40.0\ns Lx 3995.0 n2x n3x\nm1 ETMX 0.0 3.75e-05 90.0 n3x n4x\nattr ETMX mass 40.0\ns sy 4.5 n0y n1y\nm1 ITMY 0.014 3.75e-05 0.0 n1y n2y\nattr ITMY mass 40.0\ns Ly 3995.0 n2y n3y\nm1 ETMY 0.0 3.75e-05 0.0 n3y n4y\nattr ETMY mass 40.0\ns src 50.525 nbsout nsrc1\nm1 SRM 0.2 3.75e-05 90.0 nsrc1 nout\nl LO 1.0 0.0 90.0 nLO2\ns sLO1 0.0 nout nLO3\nbs bsLO 0.5 0.5 0.0 0.0 nLO3 nHD1 nHD2 nLO2\nhd TF 180.0 nHD1 nHD2\nxaxis sig f log 10 10000 1000\nfsig sig ETMX z 1.0 0.0 1.0\nfsig sig ETMY z 1.0 0.0 1.0\nyaxis log abs<\/code><\/pre><\/div><\/div><\/div><ul class=\"ssl-finesse-kat-tab-panel-tabs\"><li class=\"ssl-finesse-kat-tab-panel-tab-link ssl-finesse-kat-tab-panel-tab-link-selected\" data-tab=\"plot\">Plot<\/li><li class=\"ssl-finesse-kat-tab-panel-tab-link\" data-tab=\"script\">Script<\/li><\/ul><\/div>\n\n\n\n<p>Ok, so we get some of what looks like numerical junk at low frequencies which might be the suspensions. Let&#8217;s remove the mirror masses so suspension effects don&#8217;t apply. What does common arm look like now?<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Common arm length to output port response<\/h4>\n\n\n\n<div class=\"ssl-finesse-kat-tab-panel\" style=\"width:460px\" data-img-width=\"460\" data-img-height=\"345\"><div class=\"ssl-finesse-kat-tab-panel-tab-container\" style=\"height:345px\"><div class=\"ssl-finesse-kat-tab-panel-tab ssl-finesse-kat-tab-panel-tab-selected\" data-tab=\"plot\"><div class=\"ssl-finesse-kat-plot\"><a class=\"ssl-finesse-kat-attachmenturl\" href=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-18.svg\"><img decoding=\"async\" class=\"ssl-finesse-kat-plot-img\" src=\"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-content\/uploads\/sites\/3\/2019\/12\/plot-18.svg\"\/><\/a><\/div><\/div><div class=\"ssl-finesse-kat-tab-panel-tab\" data-tab=\"script\"><div class=\"ssl-finesse-kat-script\"><pre class=\"ssl-finesse-kat-script-input ssl-finesse-kat-script-input-display\"><code>l LI 125.0 0.0 0.0 nin\ns s1 0.0 nin nprc1\nm1 PRM 0.03 3.75e-05 90.0 nprc1 nprc2\ns prc 53.0 nprc2 nbsin\nbs bs1 0.5 0.5 0.0 45.0 nbsin n0y n0x nbsout\ns sx 4.5 n0x n1x\nm1 ITMX 0.014 3.75e-05 90.0 n1x n2x\ns Lx 3995.0 n2x n3x\nm1 ETMX 0.0 3.75e-05 90.0 n3x n4x\ns sy 4.5 n0y n1y\nm1 ITMY 0.014 3.75e-05 0.0 n1y n2y\ns Ly 3995.0 n2y n3y\nm1 ETMY 0.0 3.75e-05 0.0 n3y n4y\ns src 50.525 nbsout nsrc1\nm1 SRM 0.2 3.75e-05 90.0 nsrc1 nout\nl LO 1.0 0.0 90.0 nLO2\ns sLO1 0.0 nout nLO3\nbs bsLO 0.5 0.5 0.0 0.0 nLO3 nHD1 nHD2 nLO2\nhd TF 180.0 nHD1 nHD2\nxaxis sig f log 10 10000 1000\nfsig sig ETMX z 1.0 0.0 1.0\nfsig sig ETMY z 1.0 0.0 1.0\nyaxis log abs<\/code><\/pre><\/div><\/div><\/div><ul class=\"ssl-finesse-kat-tab-panel-tabs\"><li class=\"ssl-finesse-kat-tab-panel-tab-link ssl-finesse-kat-tab-panel-tab-link-selected\" data-tab=\"plot\">Plot<\/li><li class=\"ssl-finesse-kat-tab-panel-tab-link\" data-tab=\"script\">Script<\/li><\/ul><\/div>\n\n\n\n<p>It looks like we removed most of the numerical junk now. But it&#8217;s still non-zero.<\/p>\n\n\n\n<p>It looks to us like the path that the light takes after it splits at the beam splitter is identical. The arm cavity mirror parameters are identical, the lengths are identical. The x-arm mirrors are tuned to 90\u00b0 and the y-arm 0\u00b0, but that&#8217;s just to set the Michelson to destructively interfere common motion at the beam splitter&#8217;s output port. What else could be causing this non-zero response from common (and PRM and SRM) length changes to the output port?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Answer<\/h2>\n\n\n\n<p><em>If you know the answer, please create a new post with a link to this one, or add a comment, or ask one of the demonstrators to edit this post!<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Question The &#8220;Degrees of freedom transfer functions&#8221; task in notebook 14 involves applying signals to the cavity mirrors or the power recycling or signal recycling mirror to modulate the differential arm, common arm, power recycling and signal recycling cavity lengths, respectively. We look at a photodetector at the output port of the interferometer, which is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ssl_alp_hide_revisions":false,"footnotes":"","ssl_alp_hide_crossreferences_to":false},"categories":[1],"tags":[44],"ssl-alp-coauthor":[2],"class_list":["post-203","post","type-post","status-publish","format-standard","hentry","category-uncategorised","tag-question"],"_links":{"self":[{"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/posts\/203","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/comments?post=203"}],"version-history":[{"count":1,"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/posts\/203\/revisions"}],"predecessor-version":[{"id":217,"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/posts\/203\/revisions\/217"}],"wp:attachment":[{"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/media?parent=203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/categories?post=203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/tags?post=203"},{"taxonomy":"ssl-alp-coauthor","embeddable":true,"href":"https:\/\/logbooks.ifosim.org\/iucaa2019\/wp-json\/wp\/v2\/ssl-alp-coauthor?post=203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}